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A cylinder of height 2x cm is circumscribed by a sphere of radius 2x cm such that the circular ends of the cylinder are two small circles on the sphere. What is the ratio of the curved surface area of the cylinder to the surface area of the sphere?
  • a)
    √3 : 4
  • b)
    √3 : 3
  • c)
    √3 : 2
  • d)
    √3 : 1
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A cylinder of height 2x cm is circumscribed by a sphere of radius 2x c...

In triangle OAB, OB = height/2 = 2x/2 = x
OA = Radius of the sphere = 2x
In triangle OBA
⇒ OA2 = OB2 + AB2
⇒ (2x)2 = x2 + AB2
∴ AB = √3x = Radius of the cylinder
Ratio of Curved surface area of cylinder to the Surface area of sphere = (2π RH) ∶ (4π r2)
⇒ RH ∶ (2r2)
⇒ (√3x × 2x) ∶ [2 × (2x)2]
∴ Ratio of Curved surface area of cylinder to the Surface area of sphere = √3 : 4
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A cylinder of height 2x cm is circumscribed by a sphere of radius 2x cm such that the circular ends of the cylinder are two small circles on the sphere. What is the ratio of the curved surface area of the cylinder to the surface area of the sphere?a)√3 : 4b)√3 : 3c)√3 : 2d)√3 : 1Correct answer is option 'A'. Can you explain this answer?
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